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Survey Sampling Techniques course is one of important courses in Statisitics. Major poiuts of this course are: probability sampling, confidence intervals, Two-stage cluster sampling, Two-stage cluster sampling, estimation for mean, choosing strata, allocation across strata, ratio estimation, domain estimation, Two-stage cluster sampling. Keywords in these slides are: Finite Population Correction, Sampling Fraction, Finite Population Correction, Sampling Fraction, Population Total, Population, E
Typology: Slides
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Larger
fraction
of
population
is
sampled
Smaller
Smaller
variance
of
sample
mean
Ignoring
the
leads
to
conservative
estimate
of
the
variance
2
n N
s n
y
V
n N
1
Finite
population
correction
factor
(FPC)
However,
if
Sampling
fraction
is
very
small
(n/N
is
very
small)
FPC
is
very
close
to
1
then
FPC
has
no
practical
effect
on
the
standard
error
(SE)
or
estimated
variance
of
an
estimate
Example:
sample
of
3000
households
from
total
of
1,200,
households
(^99975).
(^00025).
1
(^000) ,
(^200) , 1
3000
1
1
(^00025). 0
(^000) ,
(^200) , 1
3000
fraction
Sampling
n N
FPC
n N
2
2
Properties
of
the
estimator
for
population
total
t
using
SRS
Assume
we
have
a
sample
of
n
SUs
from
a
population
of
SUs
Under
the
population
total
t
is
estimated
by
Under
the
estimator
for
the
total
is
an
unbiased
estimator
of
the
population
total
The
mean
of
the
sampling
distribution
for
the
sample
total
is
equal
to
the
population
total
y
N
t
tˆ
Theoretical
derivation
If
a
,^
b
are
constants
&
is
a
random
variable,
then
t y N y E N y N E t E
tˆ
b
aE
b
a
E
} ˆ { } ˆ {
ˆ
Properties
of
the
estimator
for
population
total
t
using
SRS
The
estimated
variance
for
the
total
estimator
under
is
The
estimated
variance
is
An
estimate
of
the
variance
of
the
sampling
distribution
for
the
estimated
total
under
SRS
A
measure
of
the
precision
of
the
estimated
total
as
an
estimator
of
the
population
total
1
] ˆ [ ˆ
2
2
n N
s n
N
t
V
] ˆ [ ˆ
Properties
of
the
estimator
for
population
total
t
using
SRS
The
estimated
standard
error
for
the
estimated
total
under
is
A
measure
of
the
precision
of
the
estimated
total
as
an
estimator
of
the
population
total
n N
s n
N t V t E S
1 ] ˆ [ ˆ ) ˆ ( ˆ
Properties
of
estimated
proportion
under
SRS
ˆ p
ˆp
Properties
of
estimated
proportion
under
SRS
Unbiased
estimator
for
the
variance
of
the
sampling
distribution
for
Estimator
for
SE
ˆ p
1
1
) ˆ 1 ( ˆ } ˆ { ˆ
1
1
) ˆ 1 ( ˆ } ˆ { ˆ
Quality
of
estimates
Estimator
under
a
given
design
is
unbiased
On
average
over
a
large
number
of
samples,
the
mean
of
the
estimates
“hit”
the
target
population
parameter
(centered
on
the
bull’s
eye)
Estimator
under
a
given
design
is
precise
Over
a
large
number
of
samples,
estimates
will
tend
to
be
close
to
one
another,
indicating
that
the
variance
of
the
sampling
distribution
for
the
estimator
is
small
Clump
pattern,
but
may
not
be
centered
on
bull’s
eye
(precise
but
biased)
Estimator
under
a
given
design
is
accurate
Estimator
comes
close
to
hitting
target
and
is
precise
Assess
this
with
the
mean
squared
error
(MSE)
Sometimes
we’ll
accept
a
little
bias
to
get
a
more
precise
estimator,
leading
to
a
lower
2
2
] ˆ
Bias[
] ˆ [
ˆ
ˆ
MSE
V
E
ˆ
] ˆ [
] ˆ
MSE[
then
0
] ˆ
Bias[
Population
Sampling
distribution
distribution
Basic
unit:
U={1,2,…,N}
Total
number
of
units:
N
Variable:
character
of
interest,
Y
Parameters:
characterize
the
target
population
Mean
,^
proportion
p
(central
tendency)
Total
t
Variance,
std
dev
S
2
,^
S
(spread
of
distn)
STATIC
for
a
given
Y
,^
pop
distribtn
is
the
object
of
inference
and
never
changes
with
design
or
estimator
Basic
unit:
sample
selected
using
a
specific
design
(
A
)
Total
number
of
units:
of
poss.
samples
given
design
Variable:
estimator
of
parameter,
Parameters:
characterize
the
quality
of
the
estimator
Mean
(used
to
assess
bias
of
the
estimator)
Variance,
SE
(precision
of
estimator)
DEPENDS
on
population
parameter,
estimator
of
population
parameter,
sample
design
ˆ ˆ^ } {
E
} ˆ { ˆ
}, ˆ {
E S
V
U y
docsity.com
Confidence
intervals
(CIs)
Making
inference:
a
confidence
interval
(CI)
to
express
precision
of
estimate
Need
estimated
variance
or
SE
of
estimator
for
a
population
parameter
under
a
specific,
which
provides
precision
of
the
sampling
distribution.
How
many
samples?
Number
of
possible
SRS
samples
of
size
4
from
a
population
of
size
8
Probability
of
obtaining
one
of
these
samples?
Exact
confidence
level
Interval
(not
the
usual
Note
whether
or
not
interval
covers
true
value
of
population
total,
t
intervals
cover
do
not
confidence
level
s
t
4
ˆ
